Find a pair of elements from an array whose sum equals a given number

Question

Given array of n integers and given a number X, find all the unique pairs of elements (a,b), whose summation is equal to X.

The following is my solution, it is O(nLo

Answer 1

There are 3 approaches to this solution:

Let the sum be T and n be the size of array

Approach 1:
The naive way to do this would be to check all combinations (n choose 2). This exhaustive search is O(n²).

Approach 2: 
 A better way would be to sort the array. This takes O(n log n)
Then for each x in array A, use binary search to look for T-x. This will take O(nlogn).
So, overall search is  O(n log n)

Approach 3 :
The best way would be to insert every element into a hash table (without sorting). This takes O(n) as constant time insertion.
Then for every x, we can just look up its complement, T-x, which is O(1).
Overall the run time of this approach is O(n).

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